Area of a Triangle - Explanation, Formulas, and Applications

A triangle is a type of closed polygon that has three angles, three edges, and three vertices. There are several associated concepts, such as how to find the area of triangle with 3 sides, perimeter, properties, applications, and other sister topics that kids have to learn. In this article, we will discuss a few aspects of triangles that make them one of the most incredible and widely studied geometrical shapes.

Classification of Triangles

Based on Sides

  • Equilateral Triangle: In such a type of triangle, all three sides are of equal length, and all three angles are also identical. By the sum of angles property of triangles, we conclude that all angles of an equilateral triangle are 60 degrees.
  • Isosceles Triangle: This triangle has two sides of equal length. The angles opposite these two sides are also equal in measure.
  • Scalene Triangle: In a scalene triangle all sides are of unequal measure. If two sides of a triangle are not congruent, then it forms a scalene triangle. The angles are also not equal.

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Based on Angles

  • Acute Triangle: When all the angles of a triangle are less than right angles but greater than 0 degrees, then it forms an acute triangle.
  • Right Triangle: When one of the angles measures ninety degrees, it forms a right triangle. The Pythagoras theorem is used with right triangles, especially for finding the length of an unknown side and trigonometric formulas.
  • Obtuse Triangle: When one of the angles of a triangle is greater than nighty degrees but less than 180 degrees, it is called an obtuse triangle.

Properties of Triangles

1. A triangle has exactly three sides, three angles, and three corners.

2. According to the angle sum property, all the interior angles sum up to 180 degrees.

3. All the exterior angles sum up to 360 degrees.

4. The difference in the lengths of the two sides will always be lesser than the third side.

5. The measure of the third side will always be lesser than the sum of lengths of two sides.

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Area of triangles

A few methods to find the area of a triangle are listed below.

1. Heron’s Formula

If all three sides are known, then the heron’s formula can be used to calculate the area of a triangle. This formula can be manipulated in special cases such as equilateral triangles. Suppose we have a triangle with side lengths given by d, u, and a, then the formula is written as

  • Semi perimeter, s = (d + u + a) / 2
  • Area of the scalene triangle = √[s (s – d) (s – u) (s – a)]

2. Base Height Formula

If we know the height of a triangle and the corresponding base, then you can easily find the area by this formula.

Area of a triangle = ½ × (height) × (base).

Applications

Suppose you have a patch of land that needs to be filled up with triangular tiles, then by knowing the area of each triangle, you can pick out the exact number of tiles that are needed.

Conclusion

There are several other methods that can be used to find the area of a triangle. By joining an online educational platform such as Cuemath, kids have the opportunity to gain the best quality of knowledge on triangles. They are provided with several well-organized resources to help them build a solid conceptual foundation. With such excellent guidance and exceptional tutors, kids are sure to master any topic they study.

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